Tuesday, August 13, 2013

I know what you did last summer…Trigonometric Proofs

To prove a trigonometric identity you have to show that one side of the equation can be transformed into the other side of the equation.  This usually requires turning everything into sines and cosines, some algebraic manipulations (join fractions, expand, factor, etc.) and use of fundamental trigonometric identities.  Sounds familiar? Not really, it is very different than solving equations.   You have to work on one side at a time, so algebraic properties that work on both sides of the equation can’t be used.   Complicated? Yes… but the good news about proofs is that you always know where you are going…

…and the real good news is that we are now doing it for you!  Just say the magic word (Prove, not please), type in the trig identity, press Go, and wow, a step by step poof coming your way.

Let’s start with a few examples.  With time (and practice) you’ll learn the best tricks to use and the identities that are most helpful (the Pythagorean identity is a favorite)

Example expressing with sine and cosine, Join, Factor and Pythagorean identity (click here)

Example using fraction multiplication trick (click here)

Enjoy the rest of the summer!


  1. Is anybody managing this page? If so, I'd love to get some hep with proofs. I'd even be willing to pay for it ;-)

  2. Hi, what kind of help you need?

  3. How to prove any trigo identity?
    Some tips...

  4. why does integrating sin(3x)cos(3x) dx by substitution give 2 different answers (sin^2(3x)/6) and (-cos^2(3x)/6) and apparently there is another solution using trig identities giving -1/12cos(6x) can you please explain why this is and how they all equal each other.

  5. The article you have shared here very good. This is really interesting information for me. Thanks for sharing!

  6. I know this post is old but is there a way to set the calculator so it only manipulates one particular side? For example, on some problems, the calculator will choose to manipulate the left, and the right in other situations. Is there a way to set it so it can only manipulate the left? thanks